iosr-Jm   Volume-1 ~ Issue-4

Abstract: UNIPAR FORMULAE: UNIPAR (UNI+P+AR) means UNIversal formula for Percentage by ARun. These are new innovative formulae of percentage which are applicable to all of its concepts e.g. Profit/ loss, Discount, Compound Interest, Sales Tax, Depreciation, to finding increase/decrease in population and otherconcepts also. It helps the students in dealing their daily monetary transactions in practical life.
Keywords: Compound Interest, Depreciation, Discount, Profit, Sales Tax etc.

[1] Balbir Singh (Kurdi) Mathematics class 8 English medium ( Sahibzada Ajit Singh Nagar: PSEB, 2008)
[2] Anu Soni, Mathematics class 9 English medium ( Sahibzada Ajit Singh Nagar: PSEB, 2008)
[3] R.S.Aggarwal, Quantitative Aptitude (New Delhi: S. Chand & Company, 2008)

Abstract: In this paper mainly we have obtained interesting and independent results using the equivalences L∗, R∗ and H∗.
Keywords: Union of groups, Periodic semigroup and Cancellative semigroup.

[1] Howie, J. M. Fundamentals of semigroup theory, Oxford University Press Inc., New York.

Abstract: In this paper we have obtained some interesting results on Co distributive pair in lattices. We also obtained some results on dually Co distributive pair in general lattice.
Key Words: Co distributive pair, Dually co distributive, d-prime element, Dually d-prime element, d-prime Ideals, Dually d-prime element

[1]. Gratzer,G.(1978) : "General Lattice Theory", Akademic Press, New York.
[2]. Sazsaz,Gabor(1963) : "Introduction to Lattice Theory" Akademic Press, New York and London.
[3]. Srinivas,K.V.R.(2005) : "On D-Prime Ideals of a Lattice" Bull.Cal.Math.Soc.,97(1) 79-94(2005).

Abstract: Energy is a basic necessity for the economic development of a nation. There are different forms of energy, but the most important form is the electrical energy. A modern and civilized society is so much dependent on the use of electrical energy. Electrical energy is transmitted by means of transmission lines which deliver bulk power from generating stations to load centers. The industrial development of any nation depends majorly upon the reliability of its interconnected electric power system. Availability of electric energy has been the most powerful vehicle for facilitating economic, industrial and social developments of any nation. When an electric power is generated in sufficient quantities, it needs to be transmitted in bulk to load centers and then distributed to individual consumers in proper form and quality at the lowest possible ecological and economic price. This electric power is transmitted by means of transmission lines. In this paper, we developed mathematical models for the determination of voltage and current on lossy electric power transmission lines. We derived relations which the voltage and current must satisfy on a uniform transmission line. The models contain the primary constants or parameters of the transmission line which include the series resistance (R), the shunt conductance (G), the inductance (L) and the capacitance (C). Values of these constants are specified per unit length.
Keywords: Transmission line equations, Mathematical model, Lossy transmission, Leakages in transmission line, Transmission parameters.

[1]. Aderinto, Y.O. An Optimal Control Model of the Electric Power Generating System; Unpublished Ph.D. Thesis, Department of Mathematics, University of Ilorin, Nigeria, 2010.
[2]. Atandare, D.L. Nigerian's Epileptic power supply - the way out; Prof. E.K. Obiakor Lecture Series 8, The Federal Polytechnic, Ado-Ekiti, 2007.
[3]. Bagriyanik, F.G., Aygne, Z.E. and Bagriyanik, M. Power Loss Minimization Using Fuzzy Multi-objective Formulation and Genetic Algorithm, Presented at IEEE Power Tech Conference, June 23rd 26th, Bologna, Italy, 2003.
[4]. Bamigbola, O.M. and Aderinto, Y.O. On the Characterization of Optimal Control Model of Electric power Generating Systems; International Journal of Physical Sciences, Volume4, Number 1, 2009.
[5]. Gupta, J.B. A Course in Power System; S.K. Kataria & Sons, Publisher of Engineering and Computer books, New Delhi, 2008.
[6]. Mehta, V.K and Mehta, R. Principles of Power Systems; S. Chand & Company Ltd, New Delhi, 2008.
[7]. Okafor, C.E. and Adebanji, B. An Assessment of Transmission System Reliability in Nigeria; Journal of Research in Engineering (JRENG), Vol. 6, 2009, 21-34.
[8]. Onohaebi, O.S. and Odiase, O.F. Empirical Modeling of Power Losses as a Function of Line Loadings and Lengths in the Nigerian 330KV Transmission Lines; International Journal of Academic Research, 2010, 47-53.
[9]. Wadhwa, C.L. Electrical Power Systems; New Age International (P) Limited, Publishers, New Delhi, 2009.
[10]. Williams, H.H. Jr and John, A.B. Engineering Electromagnetics; McGraw-Hill Company Ltd., New York, 2006.

Abstract: The paper provides the Abelian and Terberian theorem for generalized Mellin-Whittaker transform.
Key-words: Abeliantheorem, Generalized Mellin-Whittaker transform.

[1]. Bhosale, B. N. and Chaudhary, M. S.: Fourier-HankelTtansform of Distribution of compact support, J. Indian Acad. Math, 24(1), 2002, 169-190.
[2]. Sharma, V. D and Gudadhe, A. S.: Some Operators On Distributional Fourier-Mellin Transform, Science J.GVISH, 2, 2005, 38-42.
[3]. Kene, R. V. and Gudadhe, A. S.: On Distributional Generalized Mellin-Whittaker Transform, Aryabhata Research Journal of Physical Sciences, 12(5), 2009, 45-48.
[4]. Kene, R. V. and Gudadhe, A. S.: Some Properties of Generalized Mellin-Whittaker transform, Int. J. Contemp. Math. Sciences, 7(10), 2012, 477-488.
[5]. Zemanian, A. H.: Distribution Theory and Transform Analysis(McGraw-Hill, New York, 1965).

Abstract: This research paper deals the importance's of mathematics laboratory in teaching mathematics in high school mathematics. A total of 200 Mathematics students were involved in the study. The study is a quasi-experimental research. Results were analyzed using mean, standard deviation and analysis of covariance. It was observed that the use of mathematics laboratory enhanced achievement in mathematics. This results also showed that no significant difference exists in the achievement of male and female mathematics students taught with mathematics laboratory. By implementing this we are given more knowledge to students by concrete scene.
Key words: High school students, plane geometry, methodology class, mathematics aids.

[1]. Agwagah UNV (2001): The teaching of Number bases in Junior Secondary mathematics: The use of Base board. ABACUS: J. Math. Assoc. of Niger. (Mathematics Education Series) 26(1):1-7.
[2]. Amazigo JC.(2000): Mathematics PhobiaDiagnosis and Prescription. National Mathematical
[3]. Centre First Annual Lecture, Abuja,
[4]. July. Betiku OF (2001): Causes of Mass Failures in Mathematics Exam- inations among students. A Commissioned paper presented At Government Secondary School, Karu, Abuja Science Day, First March.
[5]. Obioma GO (1985) The Development and Validation of a Diagnostic Mathematics test for Junior Secondary Students. Unpublished doctorial dissertation, UNN. Obioma GO (2005) Emerging issues in mathematics education in Nigeria with emphasis on the strategies for effective teaching and learning of word problems and algebraic expression. J. issues Math. 8 (1), A Publication of the Mathematics Panel of the STAN, 1-8.
[6]. Obodo GC (1993) Science and mathematics Education in Nigeria (p. 120-136) Nsukka, The Academic Forum publisher. Salau MO (1995): Analysis of students' enrolment and performance in Mathematics at the senior secondary certificate level. J. Curriculum Studies.5&6(1,2): 1-8.
[7]. Srinivasa N (1978): A Laboratory for teaching mathematics. JSTAN 9(1): 22-24.
[8]. Obioma GO (2005) Emerging issues in mathematics education in Nigeria with emphasis on the strategies for effective teaching and learning of word problems and algebraic expression. J. issues Math. 8 (1), A Publication of the Mathematics Panel of the STAN, 1-8.
[9]. Obodo GC (1993) Science and mathematics Education in Nigeria (p. 120-136) Nsukka, The Academic Forum publisher. Salau MO (1995): Analysis of students' enrolment and performance in Mathematics at the senior secondary certificate level. J. Curriculum Studies.5&6(1,2): 1-8.
[10]. Srinivasa N (1978): A Laboratory for teaching mathematics. JSTAN 9(1): 22-24.

Abstract : In this paper we focus on a negative binomial (NB) regression model to take account of overdispersion in Poisson counts. Moreover, we present the power of score test for testing the overdispersion parameter in the negative binomial regression model. The power of the proposed score test was compared with the LRT and Wald test via Monte Carlo simulation technique using SAS 9.2 software. The application of the test was shown using two real datasets such as using numerical illustration and real datasets.
Keywords- Count data, Negative binomial regression, Overdispersion, Score test

[1]. J. F. Lawless, Negative binomial and mixed Poisson regression, Canadian Journal of Statistics, 15, 1987, 209-225.
[2]. C. Dean and J. F. Lawless, Tests for detecting overdispersion in Poisson regression Models, Journal of the American Statistical Association. 84, 1989, 467-472.
[3]. P. Wang, M. L. Puterman, I. Cockburn, and N. Le, Mixed Poisson regression models with covariate dependent rates. Journal of Biometrics, 52, 1996, 381-400.
[4]. I. Ozmen, Quasilikelihood/ moment method for generalized and restricted generalized Poisson regression models and its application, Journal of Biometrical, 42, 2000, 303–314.
[5]. Y. Lee, J. A. Nelder, Two ways of modeling overdispersion in non-normal data, Journal of Applied Statistics, 49, 2000, 591–598.
[6]. R. J. O'Hara Hines, A Comparison of Score Tests for Overdispersion in Generalized Linear Models. Journal of Statistical Computation and Simulation. 58, 1997, 323-342.
[7]. C. B. Dean, Testing for overdispersion in Poisson and binomial regression models. Journal of American Statistical Association. 87, 1992, 451–457.
[8]. A. C. Cameron, and P. K. Trivedi, Econometric Models Based on Count Data: Comparisons and Application of Some Estimators and Tests, Journal of Applied. Econometrics, 1, 1986, 29-53.
[9]. P. McCullagh, and J. A. Nelder, Generalized linear models (New York, USA, 2nd Ed., Chapman and Hall, 1989).
[10]. N. Jansakul, and J. P. Hinde, Linear mean-variance negative binomial models for analysis of orange tissue-culture data. Journal of Science and Technology, 26(5), 2004, 683-696.
[11]. A. C. Cameron, P.K.Trivedi, Regression Analysis of Count Data, Cambridge University Press, 1998.
[12]. P. L. Gupta, R. C. Gupta, and R. C. Tripathi, 1996, Analysis of zero-adjusted count data, Computational Statistics and Data Analysis, 23, 1996, 207-218.

Abstract: In the study of Greenhouse effect one of the important aspect of global warming is relating to increase of temperature. The factors like CO2,CO and Nitrogen etc plays a vital role to hasten the process of increase in global temperature. The only source of global warming is CO2 emission . Stochastic models are widely used in the study of global warming and its consequences. There are many aspects which are taken for study, the time to green house effect depending upon the increase of global temperature. If the global temperature crosses the threshold level which in turn leads to greenhouse effect. The threshold itself is considered to be a random variable. In this paper assuming that threshold satisfies the property known as Setting the Clock Back to Zero (SCBZ) property, the expected time to seroconversion and its variance are derived. The results are augmented with suitable numerical illustrations.
Key words: Greenhouse effect, Global warming, threshold. The AMS classification number is 92C60.

[1]. Esary, J. D., Marshall, A. W. and Proschan, I'., Shock models and wear
[2]. processes. Ann. Probability, 627-649 (1973).
[3]. Raja Rao, B., Life Expectancy for a Class of Life Distributions having the "Setting the Clock Back to Zero" property, Mathematical
Biosciences 98, 251-271 (1990).
[4]. Sathiyamoorlhi, R. and Kannan, R., Stochastic model for the time to scro-conversion of HIV transmission. Journal of Kerala
Statistical Association Vol. 12, Dec. 2001, 23-28 (2001).

Abstract: This paper presents theory and algorithm for solving a Fractional Time Transportation Problem with
Impurity Constraint (FTTPI). The aim is to minimize the maximum of the total time that the various sources take
to serve various destinations with certain amount of impurity presented in the commodities. The Fractional Time
Transportation Problem with Impurity Constraint (FTTPI) is related to Lexicographic Fractional Time
Transportation Problem with Impurity Constraint, which is solved by a lexicographic primal code. An algorithm
is proposed to obtain a global optimal solution which is explained by solving a real life example.
Keywords: Time Transportation, Fractional Programming, Impurities, Lexicographic, Optimization.

[1] L. Bandopadhyaya, Cost-time trade-off in three-axial sums transportation problem, Austral. Math. Soc. Ser. B, 35 (1994) 498505.
[2] J. Barcelo, E. Codina, J. Casas, J .L. Ferrer and D. Garcia, Microscopic traffic simulation: A tool for the design, analysis and evaluation of intelligent transport systems, Journal of Intelligent and Robotic Systems, 41 (2004) 173203.
[3] M. Basu and D.P. Acharya, On quadratic fractional generalized solid bi-criterion transportation problem", J. Appl. Math. & Computing, 10(1-2) (2002) 131143.
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[9] S. Prakash, P. Kumar, B.V.N.S. Prasad and A. Gupta, Pareto optimal solutions of a cost–time trade-off bulk transportation problem", European Journal of Operational Research, 188(1) (2008) 85100.
[10] K. Swarup, Duality in fractional programming, Unternehmensforschung, 12 (1968) 106112.
[11] A. I. Tkacenko, The generalized algorithm for Solving the fractional multi-objective transportation problem, ROMAI J. 2(1) (2006) 197-202.
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[13] A. K. Ziliaskopoulos and S.T. Waller, An Internet-based geographic information system that integrates data, models and users for transportation applications", Transportation Research Part C, 8, (2000) 427444.

Abstract: Finding applications of abstract algebra and doing research on such applications requires a certain amount of mathematical maturity on the part of the person doing the finding and researching. A strong basic grasp of set theory, mathematical induction, complementarity, and matrices is absolutely essential. This understanding is highly important. The ability to understand and analyze mathematical evidence ought to be given a larger amount of weight in the evaluation process. In this part of the lesson, we will go over the fundamentals of abstract algebra, which form the basis of the a whole course. In addition to this, we look at the principles of modern algebra and its many applications in the real world....

Key Word: Modern Algebra, Rings, Fields. Mathematical Formulation

[1]. Mahima Ranjan Adhikari, Avishek Adhikari (2012) on Basic Modern Algebra with Applications
[2]. William j. Gilbert, w. Keith nicholson (2012) on modern algebra with applications
[3]. David Joyce (2012) on Introduction to Modern Algebra
[4]. Adhikari, M.R., Adhikari, A. (2012) on Groups, Rings and Modules with Applications,
[5]. Adhikari, M.R., Adhikari, A. (2012) on Text Book of Linear Algebra: An Introduction to Modern Algebra.